On the existence of EFX allocations for goods

TL;DR

This paper proves that EFX (envy-free up to any good) allocations always exist under certain valuation function conditions for indivisible goods and multiple agents.

Contribution

It establishes the existence of EFX allocations when two agents have arbitrary set monotonic valuations and others have size monotonic valuations.

Findings

EFX allocations always exist under specified valuation conditions.

The result extends understanding of fair division with indivisible goods.

Applicable to scenarios with mixed valuation functions.

Abstract

We consider a set $E$ of $m$ indivisible goods and a set $N$ consisting of $n \geq 2$ agents. The paper shows that if two agents have \textit{arbitrary} set monotonic valuation functions and the remaining agents have size monotonic valuation functions, then EFX allocations always exist.